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A010480 Decimal expansion of square root of 24.

%I A010480 #38 Aug 21 2023 10:33:55
%S A010480 4,8,9,8,9,7,9,4,8,5,5,6,6,3,5,6,1,9,6,3,9,4,5,6,8,1,4,9,4,1,1,7,8,2,
%T A010480 7,8,3,9,3,1,8,9,4,9,6,1,3,1,3,3,4,0,2,5,6,8,6,5,3,8,5,1,3,4,5,0,1,9,
%U A010480 2,0,7,5,4,9,1,4,6,3,0,0,5,3,0,7,9,7,1,8,8,6,6,2,0,9,2,8,0,4,6,9,6,3,7,1,8
%N A010480 Decimal expansion of square root of 24.
%C A010480 Continued fraction expansion is 4 followed by {1, 8} repeated. - _Harry J. Smith_, Jun 03 2009
%C A010480 The solution to the Lane-Emden equation for a sphere of polytropic index n = 0. - _Arkadiusz Wesolowski_, Nov 11 2014
%C A010480 Using Bretschneider's formula this is the maximum area of a quadrilateral with side lengths of 1,2,3 and 4. - _Scott R. Shannon_, Jan 06 2020
%H A010480 Harry J. Smith, <a href="/A010480/b010480.txt">Table of n, a(n) for n = 1..20000</a>
%H A010480 Wikipedia, <a href="https://en.wikipedia.org/wiki/Bretschneider%27s_formula">Bretschneider's formula</a>.
%H A010480 <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>
%F A010480 Equals 2*A010464. - _R. J. Mathar_, Jan 14 2021
%F A010480 Equals 4 + Sum_{k>=0} (-1)^k * binomial(2*k,k)/((k+1) * 8^k). - _Amiram Eldar_, May 06 2022
%e A010480 4.898979485566356196394568149411782783931894961313340256865385134501920....
%t A010480 RealDigits[N[Sqrt[24],200]][[1]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 22 2011 *)
%o A010480 (PARI)  default(realprecision, 20080); x=sqrt(24); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010480.txt", n, " ", d));  \\ _Harry J. Smith_, Jun 03 2009
%Y A010480 Cf. A040019 (continued fraction). - _Harry J. Smith_, Jun 03 2009
%Y A010480 Cf. A010464, A090654.
%K A010480 nonn,cons
%O A010480 1,1
%A A010480 _N. J. A. Sloane_
%E A010480 Final digits of sequence corrected using the b-file. - _N. J. A. Sloane_, Aug 30 2009